How to remove Ubuntu One Unity indicator from the top panel in Ubuntu 12.04?
There isn't even a quit button.
I checked in the startup apps an no Ubuntu One there.
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The startup applications menu shows only a small selection of the autostart apps by default. See here for a way to display all entries, including the hidden ones: How do I add/remove the "hidden" startup applications?
After reconfiguring your startup app visibility you should be able to see a Ubuntu One entry. You can then proceed and deactivate it to stop the U1 Sync service from starting.
This will not remove the Ubuntu One messaging menu entry. Follow this guide to remove it: How can I remove "Set Up Mail" and other entries from the message indicator?
Or if you choose to completely remove U1 follow answer nr. 1 in this post: Remove ubuntu one from messaging indicator